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In the given figure, PA and PB are two t...

In the given figure, `PA` and `PB` are two tangetns to the circle with centre `O`. If `/_APB=60^(@)` then find the measure of `/_OAB`.

Text Solution

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`PA=PB` [`:'` tangents from an external point are equal]
`implies/_PAB=/_PBA=(1)/(2)xx(180^(@)-/_APB)=(1)/(2)xx(180^(@)-60^(@))=60^(@)`
Now, `/_PAO=90^(@)` [`:'` radius through the point of contact is perpendicular to the tangent]
`implies/_OAB+/_PAB=90^(@)implies/_OAB=90^(@)-/_PAB=90^(@)-60^(@)=30^(@)`.
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